Among the new US Track line products from Peco is the SL-115 HO Transition Track for Code 83 -Code 70. As most of my turnouts are Peco US Code 83 (the Code 70 turnouts are now just appearing in US hobby stores) and I like using ME Code 70 for sidings and 1950's yard trackage, I purchased a package of 4 of the new transition sections. 

Note that the SL-115 contains a short piece of wire visible from the underside of the track piece soldered to the code 70 and 83 pieces to maintain electrical continuity through the transition.

This is my initial testing of the using the SL-115 sections to join the two different brands of track with different rail sizes. It works if you take a little bit of care.  I would suggest setting up the joints on a workbench rather than doing it in place on the layout. 

There is a difference in the tie height between Peco Code 83/70 trackage and ME Code 70 track. I find that gluing strips of Evergreen #124 .020x.080 strip styrene  to the underside of the first two or three ties of the ME Code 70 track will provide an adequate shim.  This method is shown in the second photo below. Peco appears to use the same tie mold for both the Code 83 and Code 70

This is the result viewed from the top showing the ME Code 70 track on the left:

Note I used ME #26-070 Code 70/ joiners and Peco SL 110  Fine Standard rail joiners for the Code 83 track join.  I prefer the smaller ME joiners and have used their #26-083 joiners for Peco-Peco Code 83 track joins as well. 

Also shown in the photo is the HO Alignment gauge from Ribbon Rail which I find essential in keeping both Peco and Micro Engineering track straight when it needs to be straight and not bendy twisty.

This is the underside showing the .020x.080 shims glued to the ties. I used Tamiya extra thin, my usual styrene cement. The ME ties should be sanded lightly before gluing to get a better join with the styrene. 

The shims can be painted your favorite shade of RR tie brown or whatever. Presumably they will be buried in ballast. 

Peco and ME Code 70 track is a straight up join except that the shims are required for the ME track.