No.
An observance of 720 being "sharper" is DIRECTLY related to the hardware, software and source. You cannot surpass the resolution of the source (maybe if you use a detailer, but that's a whole different conversation). Most sources are at, under or around 352x480. Almost nothing aside from DV is available to the consumer in that higher res.
Macroblocks are an artifact created from lack of bitrate. 2700k is a SERIOUS lack of bitrate for 720x480, and can even be a bit to low for 352x480.
Offhand, I have no idea what the source res is for a Beta III tape. I'm not familiar with that format. It may be high res.
Your DV box only captures 720x480, DV is that res. If you saw softening of the footage at encode, blame the encoder.
If it was the Hauppauge PVR doing MPEG encoding, those boxes are slightly soft. Same for MainConcept (unoptimized) and TMPGEnc.
Double digitizing the signal (first to DV) and then to the PVR-250 was probably very damaging too. You have a DV box ... transfer it.
Hope that clears some things up for you.