There is a new Reporting API for SA360 (https://developers.google.com/search-ads/reporting). Note that this API is currently in an "open Beta"-stage, which means that the API is in a testing phase where stability is not guaranteed and some features are still missing.

We are continuously testing and changing our SA360 integration to adapt to the new API, and the goal is to release these changes as soon as the new API becomes a stable release.

When comparing SA360 data with Funnel one thing to know is that you have to compare the connected breakdowns with the same in the UI. So for example if you have connected a keyword report with no breakdowns you have to compare it to the keyword tab in the UI to get the same values as in Funnel. Or you have connected a Campaign report with the device segment you would have to go to the campaign tab and add the column device to get the same values as in Funnel. 

This happens because when adding any breakdowns to a report in SA360 both in the UI and their reporting they drop all data that doesn't contain a value for the dimension.

If you want to see the totals spend it is recommended that you connect a Campaign report with no extra segments.
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If you miss a custom SA360 metric in Funnel that is most likely because Funnel by default only brings in metrics of the types Integer and Monetary. We don't bring in by default Number and Boolean metrics. You can tell if a metric is a Number metric by its values not always being full numbers. For example 12 is considered an Integer while 12.50 would be a number.
If you wish to bring in a metric that is not yet in Funnel please reach out to support with the name of the metric and if you wish to have it for historical data.
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When reporting in a data mismatch please send in a screenshot from the SA360 with the same dimensions as the source is connected with.