It's discussions like these that remind me why I pretty much do everything I can on a cheap pcb from somewhere like dirtypcbs.... Prototype on a breadboard, carefully transpose into a schematic, lay the board out, order, and no more hand point to point soldering.
With that in mind, my $0.02....
When I do need to do stuff like this (aka a one-off prototype or I can't wait), I generally prefer the boards which pretty much mimic a breadboard.
Me and true stripboard (where you cut traces) don't get along very well. For whatever reason I've never mastered cutting traces. I seem to either not get one cut, or I slip and cut two neighboring traces. (ok, a bit of an exxageration but not much of one). Particularly evil are the ones with strips horizontally on one side and vertically on the other. Maybe I'm doing it wrong. Actually I'm probably doing it wrong.
The breadboard-style (or similar to breadboard) style makes it simple to create 'mini nodes'. Not such a big fan of the ones with the 'power stripes' down the middle of the board (under where the traces are) - too easy to create a bridge.
My second choice (and probably first for more 'analog' type designs with few IC's) is just plain perfboard without any copper on it. The ones with plated through holes (but not bare copper) are ok, but I've had too many problems related to the copper on the board. If I get a good FR4 with solder mask and plated through holes (and hasl solder on the board), then things are ok.
One note: If you get one with bare copper, get some steel wool or some of the green scrubbies and buff the copper before using it. It should be bright and shiny. If it's tarnished at all, you're going to run into issues soldering to it, and with the cheaper perfboards (phenolic paper instead of FR4), the pads will come off before the flux can clean the oxides off of the board.