Seats:The seat tube ones are way too uncomfortable for me to ride - if you don't mind the riding position though I guess it would be the best. Be great to have the wee man up front.
I have a rack mounted one - these are the sturdiest. Very robust and great on the road / smooth off road. They can transmit bumps readily to the seat, though. I recently took our lad (2 and a bit) to the top of the red at Glentress using it, then back down the forest road and it was good. I couldn't have done this when he was younger, as he would have been upset at the bumps.
A drawback is that it's a bit inflexible if you want to use your bike for other things. I have mine on a CX bike that I like to take out on proper rides - it's a pita to take off the rack each time.
The seat-tube mounted ones seem a bit flimsy to me. It's not like I've ever heard of one busted in two, so maybe it's just irrational parent concern. They're clearly less supporting than a rack though.
They must be very convenient as I can imagine you just whip them on or off as required. The stays also act as rudimentary shocks, so they may be more comfortable for the ween over the bumps.
Trailers are great, but are out for me as I have no space to store one. Expensive to buy, but hold their value well to sell as coatesy says.