Bill, it depends on the bands you're trying to run and so forth, but generally, yes, there is a difference and it can be a big one.
For example, if you try to use a coax fed 80m dipole on 40m, the impedance on 40m will be really high, the SWR on the coax will be terrible, and there will be a large increase in the loss in the coax. I have a 60 foot vertical here that has a homebrew tuner at the base. It's resonant around 3800kHz. I have a nice L network that puts it on 40m:http://n3ox.net/projects/stepperswitch/40m_match_lg.jpg
Once I tried to tune it with the tuner in the shack instead. I have about 90 feet of coax between the shack and the base of the antenna. My matching network switch had a "bypass" position, so I toggled back and forth between the tuner in the shack and the L network at the base of the antenna. The difference as measured on some broadcast carriers on 40m was about 10dB. 90% of my power was being lost in the coax when I used the shack tuner instead of the L network at the base!
To prove a point about this sort of thing I spent the evening down on 40m CW working with the shack tuner anyway. Made some nice contacts, including breaking a pileup for a station in Gambia, but all that proved was that ten watts radiated from a vertical on 40m can make some nice contacts.
Feeding a half wave vertical directly with coax (or direct coax feed of a full wave doublet like an 80m dipole on 40m) is among the WORST things you can do in terms of extra feedline loss. The only thing worse than a high impedance resonance is an antenna that's much SHORTER than a quarter wave. Like if you try to use a coax fed 80m dipole on 160m you might see 15-20dB loss!
But it all depends on the exact antenna impedance on each band you intend to use it on. Using a shack tuner to "stretch" the bandwidth of an 80m dipole across the band is no problem. The overall system performance also depends on the power you can run... if you have an amp and shack tuner and you lose 70% of your power in the feedline, you might still come out stronger than a 100W autotuner at the antenna...
Generally putting any matching device at the feedpoint is best if you need to use coax.