If you plan to do this in one survey, all respondents begin at the start of this survey, then get allocated to survey 1 or survey 2 (this can be done via a least fill quota approach that allocates the respondent to the more needy survey at the time), and then skips to the relevant block of questions (survey 1 block or survey 2 block based on the quota allocated).
So this approach has all data for survey 1 and survey 2 in the same data file.
Maybe you don't want the one survey approach? So you go with the two survey approach.
You can do this with some survey linking within termination pages.
First create your 2 surveys.
Then create a landing page survey. This is a very short survey that does the following ...
1/ Has ALL respondents directed to it with the same survey link. For this to work, you need every respondent to be allocated a unique ID or password.
2/ Include a quota variable using a least fill approach that allocates the respondent to either survey 1 or survey 2. The survey with the lower completes count at the time will be the survey the respondent is directed to.
3/ Once the quota (or the survey to complete) has been established, direct the respondent to the appropriate termination page (you can set one up for survey 1 and survey 2). When the respondent departs from the landing page survey, have them depart as an incompleted survey. Do not tick the "Terminate respondent" check box under the Settings tab of your termination question/s.
4/ The respondent now leaps out of the landing page survey to either survey 1 or survey 2.
5/ When the respondent completes survey 1 or survey 2, have them leap back in to the landing page survey. This could be a "thank you for your participation" page that appears after the termination pages that sent the respondent to survey 1 or survey 2. There is a neat feature in Sawtooth Software (sys_skipto) that helps you leap back to a desired question.
6/ Then finish off with a standard termination page that submits your survey as a completed survey.
So the map looks something like this ...
START LANDING PAGE SURVEY
ALLOCATE TO SURVEY 1 OR SURVEY 2
LEAP TO SURVEY 1 OR SURVEY 2 (AT THIS STAGE IN THE LANDING PAGE SURVEY, THE SURVEY IS AN INCOMPLETE)
COMPLETE SURVEY 1 OR SURVEY 2
LEAP BACK TO LANDING PAGE SURVEY (LEAP BACK TO A THANK YOU PAGE)
SUBMIT SURVEY AS A COMPLETE IN THE LANDING PAGE SURVEY
Come back to this post if you have any further questions. I'm hoping this has you heading in the right direction.