I have a Kat/Inv that I must admit I have him forgotten for a long time because the build I projected is soo expensive that I can't get myself to start on it. It was really fun scrapper that breezed until the 40's (my second 50 when sets were not even a rumour) and had endurance problems once I put in Focused Accuracy (when SOs came from +3 to +1 it was very noticeable with FA), but he was fun to play.
/DA is my favourite scrapper secondary and I think it can go well with Katana, but I'd prefer Kat/Inv, you can get a better performance from Kat/Inv with a minimum set investment than with Kat/DA.
If you are planning to spend loads of inf, then both will do great and I'd say go for the one that fits concept better.
I have a Kat/Dark at 37 and I can tell you that it can be painful to level. I still find Dark very draining on endurance, even with only the basic toggles going and the danger with Katana is that the quick recharge can mean you spam your attacks over and over until you're drained.
Don't get me wrong, it's a fun toon, and very, very versatile but the endurance cost alone can eat you alive. Look for +end recipies if you can. 
@Dante EU - Union Roleplayer and Altisis Victim
The Militia: Union RP Supergroup - www.themilitia.org.uk
The trouble being, every one has cottened onto impervium armor.
When I did my 1st guide I had them in there and people lauged at the fact they were only lvl 40 and I lost 2% enchancement to rez. Neve mind the +recovery and +max end. I picked up 4 sets of the 4 rez enhancing ones for about 20mil. Now you can't even get a single +resistance one for 20 mil.
So kitting out my DA/SS tank will with the 16 required IOs will set me back some where near 250mil.
As for the OP's question my answer is the same as Nightmare's, /DA if your feeling flush or /INV if you not.
I have a BS/DA is it's very very powerful. With a well thought out build my end bar hardly moves even if it does start to drop, I have conserve power for AV fights etc.
But not much in game is better that headsplitting crit on a BU, I noticed 1804 dmg to a roman the other day in one hit.....
(Quick Reply)
I lack experience with Dark Armour, so I'm not a good person to judge which combination would be best. However, it might be worth keeping in mind that Invulnerability is getting Defence debuff resistance in Issue 13 (barring any changes from the current version on Test). For a build focused on defence, this should result in a more even performance against enemies such as the Cimeroran Traitors, who will have more trouble removing all your defence.
It does depend on what enemy groups you are primarily expecting to fight though.
Kat/inv is a great combo and gets exponentially better with IOs. With my current build I can solo Cim wall with ease. Never have to use any heals whatsoever and mobs drop quite fast for a non-aoe orientated scrapper.
Also as to what you said about impervium armor, it's easy to get the whole set for under 30mil if you dont go for lvl 40 only. If you go 35-38 you'll be only a .5% or so lower than what you get at 40 and it'll cost much less.
- @DSorrow - alts on Union and Freedom mostly -
Currently playing as Castigation on Freedom
My Katana/Inv Guide
Anyone who doesn't take truth seriously in small matters cannot be trusted in large ones either. -Einstein
Would edit last post but too late; posting the numbers of different Impervium Armor sets (3 of them) that I have on my Kat/Inv:
Set 1:
Res/End: Lvl 35
Res/Rech: Lvl 35
End/Rech: Lvl 36
Res: Lvl 35
Res/End/Rech: Lvl 40
Psi Res: Lvl 20.
Total stats:
Resistance: 56.2%
Endurance: 65.4%
Recharge: 65.4%
Set2:
Res/End: Lvl 38
Res/Rech: Lvl 30
End/Rech: Lvl 36
Res/End/Rech: Lvl 40
Res: Lvl 35
Psi Res: Lvl 36
Total stats:
Resistance: 56.1%
Endurance: 66.1%
Recharge: 64.2%
Set 3:
Res/End: Lvl 36
Res/Rech: Lvl 38
End/Rech: Lvl 36
Res/End/Rech: Lvl 40
Res: Lvl 35
Psi Res: Lvl 39
Total stats:
Resistance: 56.3%
Endurance: 65.7%
Recharge: 66.1%
As you can see, you can get very good resistance values even if you dont have "40s only".
- @DSorrow - alts on Union and Freedom mostly -
Currently playing as Castigation on Freedom
My Katana/Inv Guide
Anyone who doesn't take truth seriously in small matters cannot be trusted in large ones either. -Einstein
[ QUOTE ]
I have a Kat/Dark at 37 and I can tell you that it can be painful to level. I still find Dark very draining on endurance, even with only the basic toggles going and the danger with Katana is that the quick recharge can mean you spam your attacks over and over until you're drained.
Don't get me wrong, it's a fun toon, and very, very versatile but the endurance cost alone can eat you alive. Look for +end recipies if you can.
[/ QUOTE ]
/\ This is so spot on. Even now with my rapidly approaching lvl 41 Kat/DA, end is still a huge problem... Always the first AT to call for a rest.
Main 50 & Badger Nine Claws Claws/Regen/Body
Other 50's Ph10x Brute Unjust Law Tanker Samantha Urai Scrapper Codename 1250 Scrapper
Cepheus Defender Nilus Scrapper Electro Field Blaster S.PONGE Tanker
Hmmm actually Kat/DA sounds very interesting. I think Kat/Inv is great but one of the major Katana downsides is lack of secondary effects which DA would cover to an extent.
Afraid Numina Unique, Miracle Unique, Performance Shifter chance for +end are extremely desirable for any DA.-
The cheap IO set powers then?? 
Once you manage to sort end out a bit, it is nice standing and admiring all the foes that are cowering.... before slicing and dicing!
Main 50 & Badger Nine Claws Claws/Regen/Body
Other 50's Ph10x Brute Unjust Law Tanker Samantha Urai Scrapper Codename 1250 Scrapper
Cepheus Defender Nilus Scrapper Electro Field Blaster S.PONGE Tanker
Nice as all the Kat/DA sounds as I have a lvl 50 BS/DA I think it would disapoint.
I know, fast attacks, faster animations etc etc. But BS = BIG numbers.....
I've been playing around with Mid's trying to figure which combo to go for. I'm betting on Defense bonuses (my only Scrapper is a soft capped Spines/SR, so I'm kinda spoiled) and I figured both Inv and DA can give me excellent possibilities.
I'm leaning towards /Inv just because I believe I would have less End issues. On the other hand, having 33% AoE , 28% Rng and 21% Melee (easily capped with DivAv) defences and adding the sweet resist numbers of DA+Tough and Dark Regen, makes me wonder how tough would Kat/DA be. I'd be running 10 toggles, though.
Any thoughts?
@False Fiction - Virtue / Defiant
Current projects - [Glaciologist - Ill/Cold Troller] [Cloudshaper - Storm/Dark Def] [Harald Wartooth - Elec/Psi Domi]