My group is closing in on ascension level, and I was wondering what kind of influence system to adopt.

There is an influence system described in the ascension book. But it is also possible to use a profit factor system from Rogue Trader. In Only War there is a new requisition  system also.

Anyone got any recommendation on what to go for? Is the Only War system the most updated and interesting system?

They can be used side-by-side if you like.

You'll notice that it is easier to acquire stuff with wealth than to requisition the same item with influence. That makes sense, people are always happier to give you what they want when you pay them for it :)

You could easily let your group have separate stats for Wealth (PF) and Influence. While one might boost the other, you can be influential without vast wealth, and I guess the opposite is possible too.

I do like the fact that the Influence system has modifiers for having an item permanently or just borringing it for a session or two. There are just some items that are cooler to borrow than to own. It's also a nice middlegroud between DW's Requisition and RT's Profit Factor.

I like that idea Darth Smeg. I may try and suggest we adopt a similar system. However, I would likely rule that some 'special' Ordos-Specific itmes (for instance) and only be obtained through Influence - or would be much harder to purchase through Wealth. Wealth is also a good way of representing PC non-Inquisitor side projects. Like running assassin guids and mercenary groups, smuggling Xeno tech or trading rare Amsec at auction.