I've never used a router lift, but having used an under-the-table Triton TRA-001 since day one of my routing experience, I have nothing but praise for it, but have never used it in hand held mode, Seems to me the chopping and changing would be time consuming and frustrating unless one was prepared to invest in two TRA-001s, and I'm quite satisfied with other routers I own for any hand held work.
Terry, reaching under the table to make adjustments to bit height, turn the switch off to change bit etc, I don't find to be a chore - I guess I've gotten used to it and don't need to get my head down to see under the table, just work by touch.
But when all has been said and done, it comes down to personal preference. And budget, of course!