Could you shed some light on Transaction Services in these firms? (pay/progression/exit opportunities etc.)
I'll take a shot at this. Even though I don't work in this area specifically I know a fair bit about it and people who do.
Firstly, to clarify, when you say Transaction Services are you talking about the area as a whole or specifically transaction services?
For example, EY calls their broader team Transaction Advisory Services and this captures everything from pure M&A advisory to deals modelling to real estate advisory to due diligence, whereas PwC calls the area Deals, and within deals you have M&A, real estate advisory, transaction services etc.
For the purpose of this I'll assume you mean the broader area. Pay and Career progression is in line with the broader structure of professional services firms and you can find plenty of information on this online - I'd prefer not to go into specifics.
Exit opportunities largely depend on the specific area you are in within Deals/TAS. For example you'll see people from valuations or M&A making the jump to investment banking whereas people from TS might go in-house to a Corporate Development role. Another fairly common exit is in-house strategy at a large corporate. I've also seen direct exits into small private equity firms however this is not the norm. I think when looking to exit the decision is around the type of work you want to do, obviously if you love working on live deals and want exposure to bigger deals (rather than the middle market and below where Big 4 tends to play) then IB may make sense. If you're sick of financial modelling and are looking for a role thats a mix of quantitative and qualitative tasks you'll probably get that from in-house CorpDev/Strat.
Something else to keep in mind is that TS service lines tend to be one of, if not the most competitive service lines to break into. They don't usually take many graduates or interns and the people applying are usually the same that are trying for IB. A common route is a couple of years in assurance, consulting or something else before making the switch.
Hope that answers your questions!