You should upgrade with the same service where you bought the initial subscription - Apple or Google Play.
Subscribing with different services may result in double-charges if you don't cancel your previous subscription.
iOS (Apple App Store)
You'll be charged a full price for the new subscription and Apple sends you a refund. The amount depends on how long you've used the previous subscription.
Example
You've have bought an annual Light subscription in January. When you upgrade to Standard in June, Apple charges you for the selected subscription and refunds the amount of 6 month (January-June) of your Lite subscription - you'll get half of your Lite subscription back
Android (Google Play)
An upgrade activates the subscription for a period which corresponds to the prorated amount of your previous subscription.
Example
You've bought an annual Lite subscription in January and upgrade to Standard in June. Google Play looks up the prorated amount of the remaining 6 months of Lite (July-December), calculates the time-span accordingly and activates the Standard subscription for that period.
That means you get the Standard subscription for 2,5 months. Please note that after this period the new annual Standard subscription activates for another full year.