If you have people scattered in different jurisdictions, the specific jurisdictions and the value of their travel is going to matter. This is where being penny wise is also pound foolish.
The free website solution isn't "free" if the company has to hire two worker bees to input data and manually check for travel compliance and employees are angry because it takes 6 weeks to get reimbursed.
Spend the money to hire a consultant to look at the company's unique travel profile and recommend a TA and software package which works with the company's existing accounting package and to also evaluate whether the company ought to move to a corporate card, individual responsibility corporate card or stick with personal cards. A good consultant can also look at policies which eat up a lot of time and cause a lot of angst and don't really save a lot of money. Conversely, a good consultant will also know the money pits.
Lastly, no idea what the $ volume is here, but a good consultant will also know if there are some corporate discounts to be had. Even a very small discount can add up to a big savings.
In the end, you get what you pay for.