Another option you might consider is Google Analytics App+Web.
It is a new type of Google Analytics property which is event-based (like Amplitude and Mixpanel). In App+Web you can collect exactly the same data and in the same format as the other 2 tools mentioned.
The great things about it are:
it is free
there is a free integration with BigQuery (though you'll need to pay for BigQuery, but for most SmB's it is peanuts - $5-30 a month)
Not so great:
reporting side is pretty buggy (App+Web is very new).
So if you are ok building your reporting in something like Google Data Studio, App+Web will be a great option. Your data analyst will especially be happy to have all the data in SQL format (BigQuery).
If you choose App+Web, then you can use Google Optimize (also free) as an A/B testing solution.
Google Analytics lets you measure your advertising ROI as well as track your Flash, video, and social networking sites and applications.
Heap automatically captures every user action in your app and lets you measure it all. Clicks, taps, swipes, form submissions, page views, and more. Track events and segment users instantly. No pushing code. No waiting for data to trickle in.
Amplitude provides scalable mobile analytics that helps companies leverage data to create explosive user growth. Anyone in the company can use Amplitude to pinpoint the most valuable behavioral patterns within hours.
Analysis Tools- Google Analytics is built on a powerful, easy to use, reporting platform, so you can decide what data you want to view and customize your reports, with just a few clicks.;Content Analytics- Content reports help you understand which parts of your website are performing well, which pages are most popular so you can create a better experience for your customers.;Social Analytics- The web is a social place and Google Analytics measures success of your social media programs. You can analyze how visitors interact with sharing features on your site (like the Google +1 button) and engage with your content across social platforms.;Mobile Analytics- Google Analytics helps you measure the impact of mobile on your business. Additionally, if you build mobile apps Google Analytics offers Software Development Kits for iOS and Android so you can measure how people use your app.;Conversion Analytics- Find out how many customers you're attracting, how much you're selling and how users are engaging with your site with Google Analytics' range of analysis features.;Advertising Analytics- Make the most of your advertising by learning how well your social, mobile, search and display ads are working. Link your website activity to your marketing campaigns to get the complete picture and improve your advertising performance.
Define analytics events using a simple, point 'n' click interface. People with zero coding knowledge can start tracking events and generating important metrics instantly;Automatically capture every user action in your iOS or web app and measure it all. Clicks, taps, swipes, form submissions, page views, and more;All analysis is automatically retroactive, so there's no need to wait days for data to accumulate. You can rely on each report to include everything from day one.;Define meaningful user segments in seconds, without writing code. Or pick a single user and display every single action they performed in your app.;Define active users and plot their growth, or list users who hit the sign up page but never registered.
Real-time user analytics, including funnels, retention, flexible user segmentation, and revenue analysis.; Microscope: Explore the user behavior behind any data point. Compare the behavior of engaged vs. churned users.; Growth Discovery Engine: Identify behaviors that are predictive of retention or conversion and drive explosive user growth.; Direct SQL Access via Amazon Redshift: Get access to all of your raw data with zero work on your end.