Both guys have worked very hard to make bidding easier for us!!
I'll try and take an objective shot at explaining the differences. And since you asked about bidding, I confine myself to that specific area of both programs. I use both programs because each has it's own special strengths.
The real difference between the two developers is their philosophical approach to handling the different bidding parameters. Your decision between the two programs will depend on which approach best matches your bidding objectives.
BidX uses a "filter and sorting" premise. You can filter out all your personally undesirable stuff in the bidpack. Then you sort what remains on any number of individual parameters. And you can do sequentially sorts (days off, then max credit, etc). Once you find your optimum 'sort', you then discard/trash any remaining undesirable lines and then proceed to move individual lines up/down for your final bid.
FxCal/Fx Bid Lite uses a "grading" premise and hence there are no real filters. The available sort parameters are not as extensive, but that is balanced by the ability to assign individual Grades to things like days off, cities, individual pairings, and lines and then sorting on those items. You give grades to the things that are important to you and then the sort should bring those to the top of the pile. It also has a commuting calculator (for lack of a better phrase) to help visualize how your commute applies to a given line. It also has calculated sort items like Wanted Days Off, max carryin conflict, commuting credithours, etc). It can also calculate 100 hours in 30 days to keep you from losing a good trip!!
I found that being able to assign a Grade to a desirable, individual line allows you to group similar lines together for the final up/down moves. Say you sort on max wanted days off and assign high values to each line (like maybe 100), then sort on commuting credit and see if any days off lines 'sync up' then assign a higher value to those and lower to the good commuting lines. Then when you sort on the Manual Line Grades, the higher values are at the top and you can discard/trash the stuff at the bottom. Then you do the final up/down moves for your bid.
It seems like I spent more time talking about FxCal than BidX. But since the Grading approach is 'new', it deserved a little more explanation. The grading approach does require a small mental adjustment at first, but it becomes more natural the more you do it
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You need to try both programs on a couple of bids and see which one fits your needs and preferences.