Well, Id go for the 106 GTi over the Saxo VTS and I did, becuase I had one for 2 years.
Basically the same car, I have driven the Saxos too (my sister is on her 2nd VTR), but there are a few slight differences...
The 106 is a lot rarer than the Saxo, they hold their 2nd hand value a lot better too, they also have the leather/alcantara interior (big selling point), also a leather steering wheel and gear knob (unlike plastic on Saxo), different suspension than the VTS (not as viscious with lift-off oversteer), the steering is not feather light like it is on Saxos, gearing is still close but slightly longer than a VTS and IMO better, there is a gap next to the clutch pedal to rest your foot (unlike the Saxo) and as a whole the car is generally screwed together & just trimmed/finished better than its stablemate.
Here is a shot of the interior...
http://members.lycos.co.uk/Pug106GTi/Misc/My%20106%20GTi%20Seats.jpg
Those seats are really comfy and theres plenty of space in there as I am 6 3" with size 11 feet and I had no problems. A much nicer place to be than the Saxo.
One thing to note, is that the 106 is cheaper to insure then the Saxo(wierd?!), so another tick in the box.
Handling wise the 106 is absolutely amazing and can outdrive cars costing a hell of a lot more. I have taken it on several trackdays now and you can literally hang the back end out round corners and balance it on the throttle in an almost rwd like way. Compared to a mk1 172 on track, which I did a couple of weeks ago, the 106 is sharper on the steering and slightly quicker through the corners.
Here is mine in action...
http://members.lycos.co.uk/Pug106GTi/Misc/Me_Cornering.jpg
Performance wise, they may only be a little 1.6, but do NOT underestimate them. As soon as you get these things above 5000rpm and they pull like a train all the way to 7250rpm.
The 0-60 time is just 7.4secs and it actually feels quicker due to the car being so responsive.
An easy car to tune as well, due to them being heavily restricted (both 106 & Saxo) and its not difficult to unleash a few more horses. The later cars were rumoured to have 130bhp, but this has never been proven.
They are a very easy car to live with every day too, as below the 5000rpm powerband it is quite docile and smooth. Also they are very good on fuel, even if driving quite quickly.
I recently sold this one...
http://members.lycos.co.uk/Pug106GTi/Pug%20106%20Mine%20Now%20front_side.jpg
After 2 superb years and now I really wish I hadnt!
But, I have just bought a house and I used the money from the Pug as a deposit.
We all have to grow up at some point!
Currently using my parents cars and , my old R5 GT Turbo track car, while I am forking out for washing machines, fridge freezers, setees, etc...
But wont be long until I get something else to replace the 106 (R5 is for trackdays) and I am still unsure what to get?!
Hope that helps.